at the time of writing how many elements have been discovered?

Dalton’s First list of elements, published in 1803 with other work, contained only five elements, a far cry from the 100+ that we have today.
John Dalton’s Periodic Tables

To explain the gaps, Mendeleev said that the gaps were due to undiscovered elements. In fact, his table successfully predicted the existence of gallium and germanium, which were discovered later. However, Mendeleev was never able to explain why some of the elements were out of order or why the elements should show this periodic behavior. This would have to wait until we knew about the structure of the atom.
At the time that atomic masses had been discovered, a Russian chemist named Dimitri Mendeleev was writing a textbook. For his book, he began to organize elements in terms of their properties by placing the elements and their newly discovered atomic masses in cards. He arranged the elements by increasing atomic mass and noticed that elements with similar properties appeared at regular intervals or periods. Mendeleev’s table had two problems:

References:

http://www.sussexvt.k12.de.us/science/the%20history%20of%20the%20world%201500-1899/john%20dalton%27s%20periodic%20tables.htm
http://science.howstuffworks.com/atom3.htm
http://dal.ca.libguides.com/csci/writing